Ukrainian opposition lawmaker Ilya Kiva claimed that the president "urgently" left for Poland and is hiding in the US Embassy there.
"This is where he is set to continue to utilise the Ukrainian Army and civilians while making insane orders that cost thousands of human lives", Kiva said in a video message on his Telegram channel.
Neither the Ukrainian president nor the US Embassy in Poland have commented on his claims.
Earlier, Russian State Duma speaker Vyacheslav Volodin also asserted that Zelensky fled Ukraine and headed to Poland.
"Zelensky left Ukraine. Deputies of the Verkhovna Rada said that they could not get to him in Lvov", he wrote on his Telegram channel. "He is now in Poland".
Shortly after Volodin's statement, Verkhovna Rada asserted that Zelensky did not leave Ukraine and remains in Kiev.
Several Western countries have expressed concern in regard to Zelensky's safety. Particularly, French Foreign Minister Jean-Yves Le Drian said Paris was ready "to help him if necessary". It was also reported that the United States offered him evacuation, but he refused.
Reports that Zelensky left the Ukrainian capital emerged earlier last week, with the president refuting them and posting several video messages in which he said he remained in Kiev.
In late February, Russia launched a military operation in Ukraine with the goal to "demilitarise and de-Nazify" the country. The operation began after a request for help from the Donetsk and Lugansk People's Republics. After the start of the operation, a massive wave of anti-Russian sanctions followed from the West.